Wreath Product Generalizations of the Triple (S2n,Hn,ϕ)(S_{2n},H_{n},\phi) and Their Spherical Functions

The symmetric group $S_{2n}$ and the hyperoctaheadral group $H_{n}$ is a Gelfand triple for an arbitrary linear representation $\phi$ of $H_{n}$. Their $\phi$-spherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet are always to be a Gelfand triple. Furthermore we study the relation between their spherical functions and multi-partition version of the ring of symmetric functions.Comment: 25 page

Orthogonality Relations for Multivariate Krawtchouk Polynomials

The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages, arXiv:1007.4327]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case

The Crisis of Language in Contemporary Japan: Reading, Writing, and New Technology

My dissertation is an ethnographically inspired theoretical exploration of the crises of reading and writing in contemporary Japan. Each of the five chapters examines concrete instances of reading and writing practices that have been problematized in recent decades. By calling attention to underlying moral assumptions, established sociocultural protocols, and socio-technological conditions of the everyday, I theorize the concept of embodied reading and writing thresholds. The scope of analysis is partly informed by popular discourse decrying a perceived decline in reading and writing proficiency among Japanese youth. This alleged failing literacy figures as a national crisis under the assumption that the futurity of children's national language proficiency metonymically correlates with the future well being of its national cultural body. In light of heightened interests in the past, present, and future of books, and a series of recent state interventions on the prospect of "national" text culture, it is my argument that ongoing tensions surrounding the changing media landscape and symbolic relations to the world do not merely reflect changes in styles of language, structures of spatiotemporal awareness, or forms of knowledge production. Rather, they indicate profound transformations and apprehensions among the lives mediated and embodied by the very system of signification that has come under scrutiny in the post-Lost Decade Japan (03/1991-01/2002). My dissertation offers an unique point of critical intervention into 1) various forms of tension arising from the overlapping media technologies and polarized population, 2) formations of reading and writing body (embodiment) at an intersection of heterogeneous elements and everyday disciplining, 3) culturally specific conditions and articulations of the effects of "universal" technologies, 4) prospects of "proper" national reading and writing culture, and 5) questions of cultural transformation and transmission. I hope that the diverse set of events explored in respective chapters provide, as a whole, a broader perspective of the institutional and technological background as well as an intimate understanding of culturally specific circumstances in Japan. Insofar as this is an attempt to conduct a nuanced inquiry into the culturally specific configurations and articulations of a global phenomenon, each ethnographic moment is carefully contextualized to reflect Japan specific conditions while avoiding the pitfall of culturalist assumptions. Understanding how an existing system of representation, technological imperatives and sociohistorical predicaments have coalesced to form a unique constellation is the first step in identifying how the practice of reading and writing becomes a site of heated national debate in Japan. Against theories that problematize the de-corporealizing effects of digital technology within reading and writing, I emphasize the material specificity of contemporary reading and writing practices